We consider constrained optimisation problems with a real-valued, bounded
objective function on an arbitrary space. The constraints are expressed as a
relation between the optimisation variable and the problem parameters. We assume
that there is uncertainty about these parameters. The aim is to reduce such
problems to (constrained) optimisation problems without uncertainty. We
investigate what results can be obtained for different types of parameter
uncertainty models: linear expectations, vacuous expectations, possibility
distributions, and p-boxes. Our approach is based on a reformulation as a
decision problem under uncertainty of the original problem. For the
reformulation, we investigate two different optimality criteria: maximinity and
maximality. We present some general results and simple illustrations.